| 函数系矩阵生成的分形完备簇的豪斯夺夫维数和盒维数 |
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| 引用本文： | 龙伦海,黄玲,毕红兵. 函数系矩阵生成的分形完备簇的豪斯夺夫维数和盒维数[J]. 数学学报, 2011, 54(1): 137-146 |
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| 作者姓名： | 龙伦海 黄玲 毕红兵 |
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| 作者单位： | 海南大学信息学院应用数学系 海口 570228 |
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| 基金项目： | 海南省教育厅自然科学资助项目 |
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| 摘 要： | 本文给出了函数系矩阵的定义及运算,用函数系矩阵构造了分形完备簇,并确定了相似分形完备簇在开集条件下的Hausdorff维数和Box维数.
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| 关 键 词： | 函数系矩阵 分形完备簇 Hausdorff维数及Box-维数 |
| 收稿时间： | 2010-04-13 |
| 修稿时间： | 2010-07-23 |
The Hausdorff Dimension and Box Dimension of the Complete Family of Fractals Derived by the Function System Matrix |
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| Lun Hai LONG Ling HUANG Hong Bing BI. The Hausdorff Dimension and Box Dimension of the Complete Family of Fractals Derived by the Function System Matrix[J]. Acta Mathematica Sinica, 2011, 54(1): 137-146 |
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| Authors: | Lun Hai LONG Ling HUANG Hong Bing BI |
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| Affiliation: | Department of Applied Mathematics, College of Information, Hainan University, Haikou 570228, P. R. China |
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| Abstract: | In this paper we introduce the concept and operations of the function system matrix, contruct the complete family of fractals by the function system matrix, and we determine the Hausdorff dimension and the Box-dimension of the complete family of similar fractals under the open set conditions. |
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| Keywords: | function system matrix complete family of fractals Hausdorff dimension and Box-dimension |
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